Jessica stands 150 feet from the base of a tall building. She measures the angle from her eye to the top of the building to be 84°. If her eye level is 5 feet above the ground, how tall is the building to the nearest foot?

Question

Jessica stands 150 feet from the base of  a tall building. She measures the angle from her eye to  the top of the building to be 84°. If her eye level is 5 feet above the ground, how tall is the building to the  nearest foot?

AZ · Answer

Draw an image first. Does this make sense?
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AZ · Answer

Jessica is 150 feet away from the building and she's looking from 5 feet up in the air

So when you draw the triangle, you're going to be calculating the height of the building from her eye level

You just need to make sure to add in the 5 feet when you're done

AZ · Answer

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How would you calculate 'x'

We have an angle
and we have two sides

Which two sides do we have?
Which trigonometric function would we use then? sin? cos? or tan?

KingPizza · Answer

okay I believe we would use cos, but sorry if I'm incorrect

AZ · Answer

so

SOH  CAH TOA

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

look at the triangle and the sides in relation to the angle

we have the opposite side from the angle is 'x'
and the adjacent side is going to be the 150

the hypotenuse is the longest side in a right angle triangle and it's opposite the 90 degrees

so would we use sin, cos or tan?

KingPizza · Answer

wait I'm totally misunderstanding

AZ · Answer

there you go

so can you set it up?

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

AZ · Answer

you had gotten it